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In this paper, we propose a new numerical method to find the ground state energy of a given physical system within the Kohn–Sham density functional theory. The h‐adaptive finite element method is adopted for spatial discretization and implemented with matrix‐free operator evaluation. The ground state energy is found by performing unconstrained minimization with non‐orthogonal orbitals using the limited memory Broyden–Fletcher–Goldfarb–Shanno (BFGS) method. A geometric multigrid preconditioner is applied to improve the convergence. The clear advantage of the proposed approach is demonstrated on selected examples by comparing the performance to other methods such as preconditioned steepest descent minimization. The proposed method provides a solid framework toward O(N) complexity for the locally adaptive real‐space solution of density functional theory with finite elements. [ABSTRACT FROM AUTHOR]

Chiral systems are a class of structures, which may exhibit the anomalous property of a negative Poisson's ratio. Proposed by Wojciechowski and implemented later by Lakes, these structures have aroused interest due to their remarkable mechanical properties and numerous potential applications. In view of this, this paper investigates the on-axis mechanical properties of the general forms of the flexing anti-tetrachiral system through analytical and finite element models. The results suggest that these are highly dependent on the geometry (the ratio of ligament lengths, thicknesses, and radius of nodes) and material properties of the constituent materials. We also show that the rigidity of an anti-tetrachiral system can be changed without altering the Poisson's ratio. The anti-tetrachiral system, with the unit cell shown in red. [ABSTRACT FROM AUTHOR]